Euclidean Geometry and Transformations 1st edition by Clayton Dodge – Ebook PDF Instant Download/Delivery: 0486434761 , 978-0486434766
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ISBN 10: 0486434761
ISBN 13: 978-0486434766
Author: Clayton Dodge
“A good textbook.” ― Mathematical Gazette. This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentary on the history of geometry. Contents include modern elementary geometry, isometries and similarities in the plane, vectors and complex numbers in geometry, inversion, and isometries in space. Numerous exercises appear throughout the text, many of which have corresponding answers and hints at the back of the book. Prerequisites for this text, which is suitable for undergraduate courses, include high school algebra, geometry, and elementary trigonometry. 1972 edition.
Euclidean Geometry and Transformations 1st Table of contents:
Chapter 1 Modern Elementary Geometry
1 The Beginnings of Geometry Directed Segments and Angles
2 Directed Segments and Angles
3 Ideal Points and Ratios
4 The Theorem of Menelaus
5 Ceva’s Theorem
6 Some Geometry of the Triangle
7 More Geometry of the Triangle
8 Geometric Constructions
Chapter 2 Isometries in the Plane
9 The Amazing Greeks
10 Introduction to Translations, Rotations, and Reflections
11 Introduction to Isometries
12 Transformation Theory
13 Isometries as Products of Reflections
14 Translations and Rotations
15 Halfturns
16 Products of Reflections
17 Products of Isometrie; A Summary
18 Applications of Isometries to Elementary Geometry
19 Further Elementary Applications
20 Advanced Applications
21 Analytic Representations of Direct Isometries
22 Analytic Representations of Opposite Isometries
Chapter 3 Similarities in the Plane
23 The Rebirth of Mathematical Thinking
24 Introduction to Similarities
25 Homothety
26 Similarity
27 Applications of Similarities to Elementary Geometry
28 Further Elementary Applications
29 Advanced Applications
30 Analytic Representations of Similarities
Chapter 4 Vectors and Complex Numbers in Geometry
31 The Search for the Meaning of Complex Numbers
32 Introduction to Complex Numbers
33 Vectors
34 Vectors Multiplication
35 Vectors and Complex Numbers
36 Triangles in the Gauss Plane
37 Lines in the Gauss Plane
38 The Circle
39 Isometries and Similarities in the Gauss Plane
Chapter 5 Inversion
40 Matchless Modern Mathematics
41 Inversion
42 Progressions, Ratios, and Peaucellier’s Cell
43 Inversion and Complex Geometry
44 Applications of Inversion
Chapter 6 Isometries in Space
45 What Next?
46 Introduction to Three Dimensions
47 Reflection in a Plane
48 Basic Space Isometries
49 More Space Isometries
50 Some Applications
51 Analytic Representations
Appendixes
A. A Summary of Book I of Euclid’s Elements
B. Basic Ruler and Compass Constructions
Bibliography
Hints for Selected Exercises
Answers
Index
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Tags: Clayton Dodge, Euclidean Geometry, Transformations